Syllabus
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Course Code: EP-402 Course Name: Quantum Mechanics |
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| MODULE NO / UNIT | COURSE SYLLABUS CONTENTS OF MODULE | NOTES |
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| 1 | THE ORIGIN QUANTUM PHYSICS Overview, scale of quantum physics, boundary between classical and quantum phenomena: Blackbody radiation, Planck’s quantum theory; Quantum theory of light, Photon, Photoelectric effect, Compton effect (theory and result), Frank-Hertz experiment, de-Broglie hypothesis. Davisson and Germer experiment, wave packet, phase velocity, group velocity and their relation. Heisenberg's uncertainty principle. Time energy and angular momentum, position uncertainty. Uncertainty principle from de Broglie wave. (Wave-particle duality). Gamma Ray Microscope, Electron diffraction from a slit. |
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| 2 | THE SCHRODINGER WAVE EQUATION Time dependent Schrodinger equation and dynamical evolution of a quantum state ; properties of Wave Function, Interpretation of Wave Function, probability and probability current densities in three dimensions; Condition for physical acceptability of Wave Functions. Normalization, Linearity and Superposition Principles, Eigenvalues and Eigenfunctions, Position, Linear momentum & Energy operators; commutator of position and linear momentum operators; Expectation values of position and linear momentum; Wave Function of a free Particle; Time-independent Schrodinger wave equation, Stationary states, Eigen functions, Eigen values and their significance. |
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| 3 | APPLICATION OF SCHRODINGER WAVE EQUATION TO ID PROBLEMS (i) Particle in one-dimensional box (solution of Schrodinger wave equation, Eigen functions, Eigen values, quantization of energy, nodes and anti-nodes, zero point energy). (ii) One dimensional step potential: E > Vo (reflection and transmission coefficients). (iii) One dimensional step potential: E < Vo (calculation of penetration depth). (iv) One dimensional potential barrier: E > Vo (reflection and transmission Coefficients). (v) One-dimensional potential barrier, E < Vo (calculation of reflection and penetration or tunnelling coefficients). (vi) Solution of Schrodinger equation for harmonic oscillator: energy eigen functions and eigen values, Zero-point energy. |
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| 4 | APPLICATION OF SCHRODINGER WAVE EQUATION TO 3D PROBLEMS Separation of Schrodinger wave equation in Cartesian coordinates; Free particle: energy eigenfunctions and eigenvalues; Particle in a cubic potential box: normalized energy eigenfunctions and eigenvalues, non-degenerate and degenerate eigenstates; Three-dimensional anisotropic and isotropic harmonic oscillator: normalized energy eigenfunctions and eigenvalues, degeneracy; Central potentials: Separation of Schrödinger equation in spherical polar coordinates, radial and angular equations. |
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